Question

You own two bonds, each of which currently pays semiannual interest, has a coupon rate of 6 percent, a $1,000 face value, and 6 percent yields to maturity. Bond A has 12 years to maturity and Bond B has 4 years to maturity. If the market rate of interest rises unexpectedly to 7 percent, Bond _____ will be the most volatile with a price decrease of _____ percent.

Answer 1

Answer:

see explanation

Explanation:

If the coupon rate is equal to  yields to maturity, then the bond price equal to par value of $1000.

But if the yield changes, then the price of the longer maturity bond will change more than that of the shorter maturity. Hence, Bond A will be more volatile than B.

New Price of A = PV(rate = 7%/2, nper = 12*2, pmt = 6%*1000/2, fv = 1000, 0) = $919.71, i.e. a decline of 8%

Let's check New Price of B = PV(rate = 7%/2, nper = 4*2, pmt = 6%*1000/2, fv = 1000, 0) = $965.63